Question

How do you graph `-2tan3(x - 30) + 1`?

Answer 1

See graph and details.

Explanation:

`y = - 2 tan (3 ( x - pi/ 6 ) ) +1`, asymptotic

`3 ( x - pi/ 6 ) ne { ( 2 k + 1 ) pi/2 }, k = 0, +-1, +-2, +-3, ...`

`rArr x ne { ( 2 k + 2 ) pi/6 } = { 2k ( pi/ 6 ) } ={ k (pi/3) }`

The period = the period of `tan 3x = pi/3`. See graph, with

asymptotes.
graph{(1/2(y-1)cos(3(x+pi/4))+sin(3(x+pi/4)))(x-1/3pi+0.0001y)(x+1/3pi+0.0001y)(x-2/3pi+0.0001y)(x+2/3pi+0.0001y)(x-pi+0.0001y)(x+pi+0.0001y)=0[ -4 4 -2 2]}